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Heat Transfer Engineering | Thermodynamics
The following equation will calculate the temperature on one
side of an isothermal constant temperature multilayer cylinder. The heat load
(q) conducted from the interior to the exterior layers as well as
the temperature of the interior wall (T0 or Tn) are
required as well. For each layer you must define the layer
thickness (ti) as well as the layer conductivity ki.
or
Where:
Tn = Outer surface temperature oC
T0 = Inner surface temperature oC
q = Heat flow (positive heat flow is from T0 to Tn)
ri = Outer radius of the layer i , (Meters)
ri-1 = Inner
radius of the layer i, (Meters)
ki = Thermal conductivity
of layer i, (W/m-oC)
L = Length of the cylinder (Meters)
The end walls of
the cylinder are assumed adiabatic. That is, only radial heat flow is accounted
for.
Positive values of heat (q) result in T0 being
hotter than Tn. Negative values of heat (q) result in T0
being cooler than Tn.
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